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Dynamics of vacuum states for one-dimensional full compressible Navier-Stokes equations

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  • In this paper, we consider the properties of the vacuum states for weak solutions to one-dimensional full compressible Navier-Stokes system with viscosity and heat conductivities for general equation of states. Under weak conditions on initial data, we prove that if there is no vacuum initially then the vacuum states do not occur in a finite time. In particular, the temperature variation has no immediate effects on the formation of the vacuum. There are no assumptions on density in large sets. Furthermore, we prove that two initially non interacting vacuum regions will never touch in the future.
    Mathematics Subject Classification: 35Q30, 35Q35, 76N15.}.

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